a fuzzy-based pi controller for power management of a grid...
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energies
Article
A Fuzzy-Based PI Controller for Power Managementof a Grid-Connected PV-SOFC Hybrid System
Shivashankar Sukumar 1,* ID , Marayati Marsadek 1, Agileswari Ramasamy 2, Hazlie Mokhlis 3
and Saad Mekhilef 4
1 Institute of Power Engineering (IPE), Universit Tenaga Nasional, Selangor 43000, Malaysia;[email protected]
2 Department of Electronics and Communication Engineering, Universiti Tenaga Nasional,Selangor 43000, Malaysia; [email protected]
3 Department of Electrical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia;[email protected]
4 Power Electronics and Renewable Energy Research Laboratory (PEARL), University of Malaya,Kuala Lumpur 50603, Malaysia; [email protected]
* Correspondence: [email protected]; Tel.: +60-11-53563676
Academic Editor: William HolderbaumReceived: 11 September 2017; Accepted: 16 October 2017; Published: 27 October 2017
Abstract: Solar power generation is intermittent in nature. It is nearly impossible for a photovoltaic(PV) system to supply power continuously and consistently to a varying load. Operating a controllablesource like a fuel cell in parallel with PV can be a solution to supply power to variable loads.In order to coordinate the power supply from fuel cells and PVs, a power management systemneeds to be designed for the microgrid system. This paper presents a power management systemfor a grid-connected PV and solid oxide fuel cell (SOFC), considering variation in the load and solarradiation. The objective of the proposed system is to minimize the power drawn from the grid andoperate the SOFC within a specific power range. Since the PV is operated at the maximum powerpoint, the power management involves the control of SOFC active power where a proportional andintegral (PI) controller is used. The control parameters of the PI controller Kp (proportional constant)and Ti (integral time constant) are determined by the genetic algorithm (GA) and simplex method.In addition, a fuzzy logic controller is also developed to generate appropriate control parametersfor the PI controller. The performance of the controllers is evaluated by minimizing the integral oftime multiplied by absolute error (ITAE) criterion. Simulation results showed that the fuzzy-based PIcontroller outperforms the PI controller tuned by the GA and simplex method in managing the powerfrom the hybrid source effectively under variations of load and solar radiation.
Keywords: distributed generation; fuel cell; fuzzy logic controller; hybrid system; power management;photovoltaic
1. Introduction
Renewable energy sources such as wind turbines and photovoltaics (PV) have gained prominence ingenerating electricity due to environmental concerns. A reduction in CO2 emission and the combustionof fossil fuels are among the main benefits of using these sources. At the end of 2014, renewable energysources contributed to 22.8% of global electricity production [1]. During the period of 2009–2014,the annual growth rate of solar PV capacity was higher among other renewable energy sources.Solar PV can supply a local load that is referred to as a microgrid system. The microgrid can operate inparallel with the grid or in islanded mode. In grid-connected mode, depending on both the generationand load demand, the microgrid absorbs or supplies power from/to the grid. The main challenge
Energies 2017, 10, 1720; doi:10.3390/en10111720 www.mdpi.com/journal/energies
Energies 2017, 10, 1720 2 of 17
of using PV is its dependence on the solar radiation level. Thus, it is nearly impossible to satisfya variable load since the output power from the PV varies. In order to overcome this shortcoming,a controllable source such as a fuel cell can be installed and operate in parallel with the PV. Fuel cells arechosen because of their (i) high energy conversion; (ii) zero emission of pollutant gases; (iii) noiselessoperation; and (iv) high reliability. Among other fuel cell technologies, the solid oxide fuel cell (SOFC)is an attractive option for distributed generation applications. Practical application of SOFC in powerproduction is reported in [2]. In this paper, a 100 kW SOFC unit was installed and operated for morethan 15,000 h at a power plant in Westervoort, Netherlands, proving the point that SOFC is reliableenough for commercial power generation.
A microgrid system consisting of PV and SOFC can operate in grid-connected or islanded mode.During grid-connected operation, the system should be managed well in order to coordinate powergeneration between PV and SOFC, and at the same time ensure that load demand is fulfilled. In thiscontext, an efficient power management system is required. If the total power from the hybrid systemis less than the load demand, the microgrid imports power from the grid. If the power produced fromthe hybrid source is more than the load demand, the excess power is injected into the grid. SinceSOFC is a controllable source, its output power should be regulated to its reference value specifiedby the power management system. The microgrid power management system assigns a reference setpoint for the generation units. Therefore, the generation unit should have appropriate control schemesfor their voltage source inverter (VSI) in order to position its output power to the reference pointsassigned by power management systems. It is necessary for a control scheme to attain fast responseand maintain system stability during sudden changes.
In [3] a power management strategy is developed for a hybrid system consisting of PV anda proton exchange membrane fuel cell (PEMFC) supplying power to a variable load. The authorsdeveloped a detailed model of PV, PEMFC and electrolyser. The authors used an artificial neuralnetwork (ANN) for maximum power point tracking (MPPT). They claimed that the ANN for MPPTproduced the best results for real weather conditions. Here the PEMFC is seen as a secondarygenerator which works when PV power is absent. This paper deals only with the management ofthe hybrid system, which operates in an islanded mode. Similar work was carried out in [4], wheretwo intermittent sources (PV and wind) along with a fuel cell were used to deliver DC load. Theyemployed fuzzy logic control to achieve maximum power tracking for wind and PV. The hybrid systemwas operating in islanded mode. In [5], a power management strategy for a grid-connected PV-FChybrid source was presented where the hybrid sources were operating in unit power control and feederflow control modes. The strategy is to operate PV at MPPT and the fuel cell within its power range andreduce the number of switches between the two control modes. In [3,6] a power management systemis proposed for a hybrid system consisting of PV-FC operated in islanded mode. However, the authorsdid not mention the controller used or the selection of parameters for the controller. In [7], a differentialevolution algorithm was used to find the optimal control parameters for a PI controller. The robustnessof the controller was evaluated only for the SOFC system operating in parallel with the grid. A fuzzylogic controller for tuning the PI controller parameters was designed in [8] specifically for inverterreactive power control. In [9] a PI tuning method is proposed for the energy management of a DCmicrogrid grid. The tuning of the PI controller used a swarm variant of hybrid mean variance mappingoptimization. Although they used optimization to tune the controller’s parameters, it may be difficultto implement this in real time. An optimal controller was presented in [10] for a grid-connectedmicrogrid operation considering changes in the load. In this work, the control parameters weretuned using the particle swarm optimization (PSO) technique. The operating range of the distributedsource, a constraint, was not considered, and the robustness of the controller was demonstrated fora single step change in the load. In addition, the reference set point which was given as an inputto distributed generator’s (DG) control was fixed. From the above references, it can be confirmedthat many researchers focused on the design of power management for the operation of hybridsystems. However, there is very limited research that focuses on the selection of control parameters
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for the distributed generator’s (DG) real power controllers. Moreover, most of it only considers caseswhere DG output is constant. Hence, there is a need to look into this matter, which will be addressedin this paper.
Fuzzy logic is mathematical tool which provides solutions for a complex problem where thereis no well-defined mathematical formulation. Mamdani and Takagi Sugeno interface fuzzy systemsare commonly used for control applications. An application of a mamdani interface system is foundin [11] where a fuzzy-based speed governor was designed for a mini hydro power plant that suppliesvarying load. In [12] an adaptive fuzzy logic controller was designed using a mamdani interfacesystem for load frequency control of a small hydro plant. Some applications of Takagi Sugeno fuzzysystems are presented in [13,14]. In [13], a Takagi Sugeno fuzzy system is designed to efficientlycontrol static synchronous compensator (STATCOM) installed in a power system network undervarious disturbances. The voltage and frequency of an isolated wind turbine controlled by a TakagiSugeno fuzzy logic controller considering variation in wind speed and load power can be foundin [14]. A fuzzy logic system integrated with an optimization technique to provide fast and robustresults has been presented in [15–18]. In [15], a fuzzy-logic–genetic-algorithm model is developed toestimate monthly solar radiation. The results presented in [15] indicate that the fuzzy–genetic modelmore accurately estimates the monthly solar radiation than an artificial neural network (ANN) andneuro fuzzy model. The application of a fuzzy-based controller to tune the PI control parameters fora hybrid electric vehicle application is found in [16]. A cuckoo-search-optimization-based fuzzy logiccontroller is developed in [17] to operate a hybrid system consisting of PV, battery and diesel generatorin standalone mode. PSO used to tune the membership function of a fuzzy controller for solar PVMPPT control is carried out in [18]. Application of fuzzy logic to solve diverse engineering problemscan be found in the literature; however, the application of fuzzy to find the PI controller parameters fora DG used in a power management problem is very limited.
In this paper, a power management algorithm is developed for a grid-connected PV-SOFC hybridsystem, taking into consideration variation in the load and solar radiation. When the system is inoperation, the power management system facilitates PV to operate at the maximum power point,minimizing the power drawn from the grid and operating the fuel cell within its operating efficiency.The control of the power from the hybrid source is possible by controlling the power output fromthe SOFC system. Here, a PI controller is employed to control the active power flow from the SOFCsystem. A fuzzy logic system, genetic algorithm and simplex are designed to obtain the optimalcontrol parameters (Kp and Ti) for the PI controller, taking into consideration variation in the load andsolar radiation. The integral of time multiplied by absolute error (ITAE) criterion is used to evaluatethe performance of the controllers. The SOFC operates within a specific power range (PFCmin,PFCmax). The simulation model of the grid-connected PV-SOFC was built in PSCAD software.
2. System Description
The proposed microgrid incorporates two electronically-interfaced distributed generators (DG)connected through a three-phase voltage source converter (VSC). A 100 kW SOFC is the primarypower source. Since minimizing the power drawn from the grid is considered as one of the objectives,the SOFC is sized to the peak load where the fuel cell is able to supply power to the variable load inthe absence of PV. The load demand varies throughout 24 h. A 200 kW PV is also connected wherethe available power is injected into the microgrid system with a unity power factor. The microgridoperates in grid-connected mode.
2.1. Hybrid Grid-Connected PV-SOFC System
The microgrid system considered here consists of a 200 kW PV array and 100 kW SOFC connected tothe point of common coupling through a 0.4/11 kV transformer (Figure 1). The system is grid-connectedand operates in parallel with variable load.
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Figure 1. Grid‐connected hybrid system.
2.2. PV Array Model
An electrical equivalent of solar cell is modeled by connecting a current source anti‐parallel with
a diode which is shown in Figure 2 [19].
Figure 2. Equivalent circuit of single diode solar cell.
When solar radiation falls on a solar cell, a DC photo current (Ip) is generated. Ip varies
proportionally with changes in solar radiation. Applying Kirchhoff’s current law to the equivalent
circuit gives [20],
shdp IIII (1)
The diode current (Id) can be calculated as,
sh
s
c
sod R
IRV
qnkT
IRVII ]1
/[exp (2)
Io is the dark current and can be calculated as,
nk
qe
TTT
TII g
ccrefcref
corefo
11exp3
3
(3)
where,
Ioref: dark current at Tcref;
k: Boltzman constant;
eg: band gap energy;
Tcref: reference cell temperature;
Tc: cell temperature;
Figure 1. Grid-connected hybrid system.
2.2. PV Array Model
An electrical equivalent of solar cell is modeled by connecting a current source anti-parallel witha diode which is shown in Figure 2 [19].
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Figure 1. Grid‐connected hybrid system.
2.2. PV Array Model
An electrical equivalent of solar cell is modeled by connecting a current source anti‐parallel with
a diode which is shown in Figure 2 [19].
Figure 2. Equivalent circuit of single diode solar cell.
When solar radiation falls on a solar cell, a DC photo current (Ip) is generated. Ip varies
proportionally with changes in solar radiation. Applying Kirchhoff’s current law to the equivalent
circuit gives [20],
shdp IIII (1)
The diode current (Id) can be calculated as,
sh
s
c
sod R
IRV
qnkT
IRVII ]1
/[exp (2)
Io is the dark current and can be calculated as,
nk
qe
TTT
TII g
ccrefcref
corefo
11exp3
3
(3)
where,
Ioref: dark current at Tcref;
k: Boltzman constant;
eg: band gap energy;
Tcref: reference cell temperature;
Tc: cell temperature;
Figure 2. Equivalent circuit of single diode solar cell.
When solar radiation falls on a solar cell, a DC photo current (Ip) is generated. Ip variesproportionally with changes in solar radiation. Applying Kirchhoff’s current law to the equivalentcircuit gives [20],
I = Ip − Id − Ish (1)
The diode current (Id) can be calculated as,
Id = Io[exp(
V+IRsnkTc/q
)− 1]−
(V+IRs
Rsh
)(2)
Io is the dark current and can be calculated as,
Io = Iore f
(Tc
3
Tcre f3
)exp[(
1Tcre f− 1
Tc
)]qegnk (3)
where,
Ioref: dark current at Tcref;
k: Boltzman constant;eg: band gap energy;Tcref: reference cell temperature;
Tc: cell temperature;q: electron charge;
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n: diode ideality factor.
Ip depends on solar radiation and temperature and can be expressed as,
Ip = ISCre fG
Gre f
[1 + αt
(Tc − Tcre f
)](4)
where,
Gref: reference solar radiation;
αt: temperature coefficient of photo current.
PV cells are connected in series/parallel combination to make the PV module. The PV modulesare arranged in series and in parallel combination to generate the required electrical power. A 200 kWPV plant is built by connecting 40 strings in parallel where each string contains 20 modules in a series.The electrical specifications of the PV module is obtained from [21].
The MPPT controller connected to the DC/DC converter of PV always captures the maximumpower from a solar cell. MPPT algorithms such as incremental conductance (IC), perturbation andobservation (P&O), and constant voltage are the common techniques found in the literature. Amongthese techniques, the IC algorithm is the simplest and most effective technique that is used widely.The IC algorithm is the fastest in MPPT under rapid weather changing conditions and the poweroscillation is negligible at the maximum power point [22]. For this reason, the IC algorithm method isused in this work.
2.3. SOFC Model
The SOFC is a distributed generator (DG) technology that generates power from chemicalreactions. The advantages of using SOFC over other fuel cells are long term stability and fuel flexibility;the electrical efficiency of a typical SOFC power plant can reach up to 70% [23]. A grid-connected SOFCdeveloped using PSCAD software is presented in [24]. The output fuel cell stack voltage consideringohmic loss is given by [25],
V = No[
Eo + RT2F
(ln
pH2 p0.5O2
pH2O
)]− rI f c (5)
where,
Ifc: fuel cell current;
R: universal gas constant;T: absolute temperature in kelvin;PH2 , PO2 and PH2O: partial pressure of hydrogen, oxygen and water;r: representation of ohmic loss in ohm;F: Faraday’s constant;Eo: ideal standard potential;No: number of cells in series in the stack.
The utilization factor and temperature of the stack are critical operating variables of SOFC.The utilization factor is the ratio between fuel consumed to total fuel input and the range of the utilizationfactor should be 80–90% [26]. For this work, the utilization factor is taken as a constant value of 85%and the operating temperature is kept constant at 1273 K [26]. The parameters of the 100 kW SOFCpower plant are obtained from [27].
3. Proposed Operating Strategy of Hybrid System
The hybrid system supplies power at a variable load throughout the day. The power managementsystem coordinates DG output (in this case PV and SOFC) in order to supply the variable load. In this
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operating strategy, the power from SOFC is regulated to its reference value. To coordinate the PV-SOFCoperation, an appropriate reference value must be set to the operating constraints of the DGs. Oncethe SOFC operating limit is known, the operating strategy depends on load variation and PV outputpower. When hybrid power supplies the load in grid-connected mode, the power balance equation isgiven by,
PPV + PFC + PGRID = PLOAD (6)
Since the power drawn from the grid (PGRID) incurs costs, the PGRID has to be minimized.Therefore the value of PGRID is set to zero.
PPV + PFC = PLOAD (7)
The operating limit of SOFC output power is given as follows,
PHYre f = PPV + PFCre f (8)
In Equation (7), when PV output (PPV) varies, the balance power is compensated by SOFC (PFC).The fuel cell supplies power based on its reference value (PFCref). Therefore, the total power fromthe hybrid generators is regulated to its reference value (PHYref). The reference of the hybrid system isgiven by,
PHYre f = PPV + PFCre f (9)
Figure 3 shows the operating strategy of a fuel cell when PPV equals zero. The references for fuelcell and hybrid system generation are given in Equations (10) and (11), respectively.
PiFCre f = Pi
Load, i = 0, 1, 2, 3, . . . n (10)
PiHYre f = P0
PV + PiFCre f , i = 0, 1, 2, 3, . . . n (11)
In the absence of PPV generation, only the fuel cell has to supply power to the varying load. Forexample, when load demand increases from PLoad 1 to PLoad 2, the change in the load is assigned asthe fuel cell reference set point (PFCref 2). Therefore, the SOFC delivers the required power (PFC 2)following the reference set point. Since the PV is absent, the total power generated from the hybridsource is equal to PFCref 2. In this way, if the load demand reaches the maximum value PLoad n, which is100 kW, fuel cell generation is also increased to its maximum capacity PFCmax following its referencePFCref n. For load increment or decrement, the change in PFCref and PHYref is shown in Figure 3. It shouldbe noted that PLoad 0 is the load demand equal to or less than 20 kW. Here, the power from the SOFC isfixed at PFCmin i.e., 20 kW.
When PPV is greater than zero, the operating strategy depends on PV output power and loadvariation. PV power and load variation are time dependent. In the case when PV power is available butless than the load, the SOFC supplies the deficit in power and the power from the grid is maintained atzero in order to reduce the cost for the power drawn from the utility grid. Therefore the target hybridreference power is given as,
PHYre f (t) = PPV(t) + PFCre f (t) + PGrid(t) (12)
where,PFCre f (t) = PLoad(t)− PPV(t), PGrid(t) = 0 (13)
In the case where PV power is more than the load, the excess power is injected into the grid wherethe value will be negative. In this case the fuel cell power PFCref is fixed to a minimum operating point(PFCmin), that is, 20 kW in order to avoid the underused condition, as this will lead to unexpected highcell voltages. Then the target reference power is given as,
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PHYre f (t) = PPV(t) + PFCre f (t) + PGrid(t) (14)
where,PFCre f (t) = 20 kW, PGrid(t) = PLoad(t)− PPV(t) (15)
It should be noted that the PFC is operated taking into consideration the constraint as stated inEquation (8). The complete control algorithm for the power management module is shown in Figure 4.
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variable load. In this operating strategy, the power from SOFC is regulated to its reference value. To
coordinate the PV‐SOFC operation, an appropriate reference value must be set to the operating
constraints of the DGs. Once the SOFC operating limit is known, the operating strategy depends on
load variation and PV output power. When hybrid power supplies the load in grid‐connected mode,
the power balance equation is given by,
LOADGRIDFCPV PPPP (6)
Since the power drawn from the grid (PGRID) incurs costs, the PGRID has to be minimized. Therefore
the value of PGRID is set to zero.
LOADFCPV PPP (7)
The operating limit of SOFC output power is given as follows,
FCrefPVHYref PPP (8)
In Equation (7), when PV output (PPV) varies, the balance power is compensated by SOFC (PFC).
The fuel cell supplies power based on its reference value (PFCref). Therefore, the total power from the
hybrid generators is regulated to its reference value (PHYref). The reference of the hybrid system is
given by,
FCrefPVHYref PPP (9)
Figure 3 shows the operating strategy of a fuel cell when PPV equals zero. The references for fuel
cell and hybrid system generation are given in Equations (10) and (11), respectively.
… 3, 2, 1, 0,= , niPP iLoad
iFCref (10)
… 3, 2, 1, 0,= ,0 niPPP iFCrefPV
iHYref (11)
In the absence of PPV generation, only the fuel cell has to supply power to the varying load. For
example, when load demand increases from PLoad 1 to PLoad 2, the change in the load is assigned as the
fuel cell reference set point (PFCref 2). Therefore, the SOFC delivers the required power (PFC 2) following
the reference set point. Since the PV is absent, the total power generated from the hybrid source is
equal to PFCref 2. In this way, if the load demand reaches the maximum value PLoad n, which is 100 kW,
fuel cell generation is also increased to its maximum capacity PFCmax following its reference PFCref n. For
load increment or decrement, the change in PFCref and PHYref is shown in Figure 3. It should be noted
that PLoad 0 is the load demand equal to or less than 20 kW. Here, the power from the SOFC is fixed at
PFCmin i.e., 20 kW.
Figure 3. Operating strategy of fuel cell when PPV0 = 0. Figure 3. Operating strategy of fuel cell when PPV0 = 0.
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When PPV is greater than zero, the operating strategy depends on PV output power and load
variation. PV power and load variation are time dependent. In the case when PV power is available
but less than the load, the SOFC supplies the deficit in power and the power from the grid is
maintained at zero in order to reduce the cost for the power drawn from the utility grid. Therefore
the target hybrid reference power is given as,
)()()()( tPtPtPtP GridFCrefPVHYref (12)
where,
)()()( tPtPtP PVLoadFCref , 0)( tPGrid (13)
In the case where PV power is more than the load, the excess power is injected into the grid
where the value will be negative. In this case the fuel cell power PFCref is fixed to a minimum operating
point (PFCmin), that is, 20 kW in order to avoid the underused condition, as this will lead to unexpected
high cell voltages. Then the target reference power is given as,
)()()()( tPtPtPtP GridFCrefPVHYref (14)
where,
kW20)( tPFCref , )()()( tPtPtP PVLoadGrid (15)
It should be noted that the PFC is operated taking into consideration the constraint as stated in
Equation (8). The complete control algorithm for the power management module is shown in Figure
4.
Figure 4. Control algorithm for power management system.
Figure 4. Control algorithm for power management system.
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4. Methodology
4.1. Control of SOFC Voltage Source Inverter (VSI)
The voltage and active power flow from the inverter output is regulated by adjusting the modulationindex and phase angle of the inverter, respectively. Regulating the inverter terminal voltage determinesthe reactive power flow as well. During the operating strategy, the fuel cell reference value can beachieved by controlling fuel cell power to the desired level. The PI controller is employed for betterdynamic response. In this paper, PI controllers are utilized to generate the modulation index andphase angle. From Figure 5, the active power from the fuel cell output is controlled by controlling itsdirect sequence component. From the meter installed at the inverter output, the actual output power iscalculated and is compared with its reference, which is produced from the power management system.The error signal of the active power is given as the input to the PI controller. The controller generatesa reference direct axis component from the error signal and is fed into dq0 to abc transformationblock. Finally the control signals for the inverter are generated by the pulse width modulation(PWM) technique.
This work focuses on implementing fuzzy logic to generate appropriate control values for a realpower controller where the real power error signal is given as an input to the MATLAB-fuzzy interfacesystem (FIS) system. The FIS system in turn generates the appropriate proportional gain (Kp) andintegral time constant (Ti) which are then used as input for the PI controller. Here, the SOFC referenceset point (PFCref) is generated from the power management system module.
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4. Methodology
4.1. Control of SOFC Voltage Source Inverter (VSI)
The voltage and active power flow from the inverter output is regulated by adjusting the
modulation index and phase angle of the inverter, respectively. Regulating the inverter terminal
voltage determines the reactive power flow as well. During the operating strategy, the fuel cell
reference value can be achieved by controlling fuel cell power to the desired level. The PI controller
is employed for better dynamic response. In this paper, PI controllers are utilized to generate the
modulation index and phase angle. From Figure 5, the active power from the fuel cell output is
controlled by controlling its direct sequence component. From the meter installed at the inverter
output, the actual output power is calculated and is compared with its reference, which is produced
from the power management system. The error signal of the active power is given as the input to the
PI controller. The controller generates a reference direct axis component from the error signal and is
fed into dq0 to abc transformation block. Finally the control signals for the inverter are generated by
the pulse width modulation (PWM) technique.
This work focuses on implementing fuzzy logic to generate appropriate control values for a real
power controller where the real power error signal is given as an input to the MATLAB‐fuzzy
interface system (FIS) system. The FIS system in turn generates the appropriate proportional gain (Kp)
and integral time constant (Ti) which are then used as input for the PI controller. Here, the SOFC
reference set point (PFCref) is generated from the power management system module.
Figure 5. Solid oxide fuel cell (SOFC) active power control.
The PI controller used in the SOFC active power control should be robust in nature when the
system is operating under dynamic changes such as PV output and load. Therefore, optimal
operation of the PI controller is necessary. The optimal values for the real power controller Kp and Ti
is determined using a fuzzy logic controller. For comparison, the GA and simplex method were also
used to determine the control parameters of the PI controller. In this work, the controller’s objective
function is to minimize the error using the ITAE performance criterion. The advantage of using the
ITAE performance criterion is that it produces smaller overshoot and oscillations [28]. The
mathematical expression for the ITAE criterion is given as:
dttetJ ).)(.(0
(16)
where,
t is the time;
Figure 5. Solid oxide fuel cell (SOFC) active power control.
The PI controller used in the SOFC active power control should be robust in nature whenthe system is operating under dynamic changes such as PV output and load. Therefore, optimaloperation of the PI controller is necessary. The optimal values for the real power controller Kp and Ti isdetermined using a fuzzy logic controller. For comparison, the GA and simplex method were also usedto determine the control parameters of the PI controller. In this work, the controller’s objective functionis to minimize the error using the ITAE performance criterion. The advantage of using the ITAEperformance criterion is that it produces smaller overshoot and oscillations [28]. The mathematicalexpression for the ITAE criterion is given as:
J =∞∫0(t.|e(t)|).dt (16)
where,
t: time;
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e(t): the difference between reference power and the actual fuel cell power.
To increase the robustness of the controller, the optimization is performed on all hourly datafor the entire day, which means that the ITAE index is optimized for 24 different operating points.Therefore, Equation (14) is rewritten for 24 different operating points. The objective function is given as,
J =24∑
n=0
∞∫0(t.|e(t)|).dt, n = 0, 1, 2, . . . 24 (17)
4.2. Proposed Fuzzy-Based PI Controller Model
The fuzzy-based PI controller was modeled in the PSCAD environment using the SOFC-fuzzyinterface system (FIS). Figure 6 shows a block diagram of the fuzzy-logic-based PI control. A FORTRANsubroutine was written in PSCAD to interface with the MATLAB engine.
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e(t) is the difference between reference power and the actual fuel cell power.
To increase the robustness of the controller, the optimization is performed on all hourly data for
the entire day, which means that the ITAE index is optimized for 24 different operating points.
Therefore, Equation (14) is rewritten for 24 different operating points. The objective function is given
as,
24 ... 2, 1, 0, = ,|).)(|.(24
0 0
ndttetJn
(17)
4.2. Proposed Fuzzy‐Based PI Controller Model
The fuzzy‐based PI controller was modeled in the PSCAD environment using the SOFC‐fuzzy
interface system (FIS). Figure 6 shows a block diagram of the fuzzy‐logic‐based PI control. A
FORTRAN subroutine was written in PSCAD to interface with the MATLAB engine.
Figure 6. Block diagram for fuzzy‐based proportional and integral (PI) control.
The MATLAB‐FIS system has one input (PFCref) and two outputs (Kp and Ti). The FIS system
receives PFCref as the input signal, and depending on the input signal an appropriate control parameter
is sent back to the SOFC active power controller in the PSCAD environment. The FIS system consists
of three important steps: (i) fuzzification; (ii) rule base mechanism; and (iii) defuzzification. As a first
step, a set of input data (PFCref) are converted into a fuzzy set using a membership function. A
membership function is used in the fuzzification and defuzzification process where the set of non‐
fuzzy inputs is mapped to fuzzy sets. For this work, a triangular membership function was
constructed for PFCref, Kp and Ti, given in Figure 7. The linguistic variables of input PFCref are denoted
as Ref 1 to Ref 8, shown in Figure 7a. The linguistic variables of the output are indicated as Kp1 to Kp5
for Kp in Figure 7b and Ti1 to Ti5 for Ti in Figure 7c, respectively.
(a)
(b)
Figure 6. Block diagram for fuzzy-based proportional and integral (PI) control.
The MATLAB-FIS system has one input (PFCref) and two outputs (Kp and Ti). The FIS systemreceives PFCref as the input signal, and depending on the input signal an appropriate control parameteris sent back to the SOFC active power controller in the PSCAD environment. The FIS system consists ofthree important steps: (i) fuzzification; (ii) rule base mechanism; and (iii) defuzzification. As a first step,a set of input data (PFCref) are converted into a fuzzy set using a membership function. A membershipfunction is used in the fuzzification and defuzzification process where the set of non-fuzzy inputs ismapped to fuzzy sets. For this work, a triangular membership function was constructed for PFCref, Kp
and Ti, given in Figure 7. The linguistic variables of input PFCref are denoted as Ref 1 to Ref 8, shownin Figure 7a. The linguistic variables of the output are indicated as Kp1 to Kp5 for Kp in Figure 7b andTi1 to Ti5 for Ti in Figure 7c, respectively.
Energies 2017, 10, 1720 9 of 17
e(t) is the difference between reference power and the actual fuel cell power.
To increase the robustness of the controller, the optimization is performed on all hourly data for
the entire day, which means that the ITAE index is optimized for 24 different operating points.
Therefore, Equation (14) is rewritten for 24 different operating points. The objective function is given
as,
24 ... 2, 1, 0, = ,|).)(|.(24
0 0
ndttetJn
(17)
4.2. Proposed Fuzzy‐Based PI Controller Model
The fuzzy‐based PI controller was modeled in the PSCAD environment using the SOFC‐fuzzy
interface system (FIS). Figure 6 shows a block diagram of the fuzzy‐logic‐based PI control. A
FORTRAN subroutine was written in PSCAD to interface with the MATLAB engine.
Figure 6. Block diagram for fuzzy‐based proportional and integral (PI) control.
The MATLAB‐FIS system has one input (PFCref) and two outputs (Kp and Ti). The FIS system
receives PFCref as the input signal, and depending on the input signal an appropriate control parameter
is sent back to the SOFC active power controller in the PSCAD environment. The FIS system consists
of three important steps: (i) fuzzification; (ii) rule base mechanism; and (iii) defuzzification. As a first
step, a set of input data (PFCref) are converted into a fuzzy set using a membership function. A
membership function is used in the fuzzification and defuzzification process where the set of non‐
fuzzy inputs is mapped to fuzzy sets. For this work, a triangular membership function was
constructed for PFCref, Kp and Ti, given in Figure 7. The linguistic variables of input PFCref are denoted
as Ref 1 to Ref 8, shown in Figure 7a. The linguistic variables of the output are indicated as Kp1 to Kp5
for Kp in Figure 7b and Ti1 to Ti5 for Ti in Figure 7c, respectively.
(a)
(b)
Figure 7. Cont.
Energies 2017, 10, 1720 10 of 17Energies 2017, 10, 1720 10 of 17
(c)
Figure 7. (a–c) shows the membership function for PFCref, Kp and Ti, respectively.
A rule‐based mechanism was created to find the output variable for the given input. The fuzzy
rule constructed for this work is shown in Table 1. The rule‐based mechanism has a simple if–then
statement with a condition and conclusion.
Table 1. Rules for fuzzy logic controller.
PFCref
Ref 1 Ref 2 Ref 3 Ref 4 Ref 5 Ref 6 Ref 7 Ref 8
Kp Kp1 Kp1 Kp2 Kp2 Kp3 Kp3 Kp4 Kp5
Ti Ti1 Ti1 Ti2 Ti2 Ti3 Ti3 Ti4 Ti5
With the help of the output membership function, the resulting fuzzy set is mapped to its output.
The appropriate Kp and Ti from the FIS system is sent back to the PSCAD environment. The advantage
of using fuzzy logic is that for any change in the PFCref, a specific value for the PI controller parameters
is produced. The methodology proposed in this paper is the design of a fuzzy controller to generate
appropriate the real power PI controller control parameters considering ITAE as the performance
criterion. The possible limitation of the proposed method is that the fuzzy controller solution is
specifically for the ITAE performance criterion. However, the fuzzy controller may provide varying
solutions if different performance criteria, such as integral absolute error (IAE), and integral square
error (ISE), were used.
On the whole, a power management system for a grid‐connected hybrid system consisting of
solar PV and SOFC is proposed considering varying loads and solar radiation. In order to operate the
SOFC efficiently within a specific power range and to deliver the power set by the reference set point,
a fuzzy logic controller is also developed to generate appropriate control parameters for the PI
controller. The performance of the controllers is evaluated by the minimizing ITAE criterion for a 24
h time period.
5. Simulation Results
5.1. Optimization of Control Parameters
The objective of the SOFC active power controller is to deliver a power set by the reference
(PFCref), which is generated from the power management module. The control parameters of the
controller are evaluated using the GA and simplex method. The PSCAD program is equipped with
the optimum run search engine module, which enables us to perform successive simulations for a
group of parameters. The group of parameters generated by the optimization algorithm is used for
simulation program and simultaneously evaluates the objective function given in Equation (14). The
GA and simplex method present in the optimum run module were used for this study. A generalized
simulation flow for the GA and simplex method is presented in Figure 8. The search is terminated
when the stopping criterion is met, that is, when the algorithm completes the maximum number of
iterations.
The fuel cell reference set point (PFCref) changes at regular intervals due to changes in load and
PV input power. The PI controller parameters are optimized for the SOFC reference set points (PFCref)
for every hour. The final optimized values for different fuel cell reference set points are used for the
Figure 7. (a–c) shows the membership function for PFCref, Kp and Ti, respectively.
A rule-based mechanism was created to find the output variable for the given input. The fuzzyrule constructed for this work is shown in Table 1. The rule-based mechanism has a simple if–thenstatement with a condition and conclusion.
Table 1. Rules for fuzzy logic controller.
PFCref
Ref 1 Ref 2 Ref 3 Ref 4 Ref 5 Ref 6 Ref 7 Ref 8
Kp Kp1 Kp1 Kp2 Kp2 Kp3 Kp3 Kp4 Kp5Ti Ti1 Ti1 Ti2 Ti2 Ti3 Ti3 Ti4 Ti5
With the help of the output membership function, the resulting fuzzy set is mapped to its output.The appropriate Kp and Ti from the FIS system is sent back to the PSCAD environment. The advantageof using fuzzy logic is that for any change in the PFCref, a specific value for the PI controller parametersis produced. The methodology proposed in this paper is the design of a fuzzy controller to generateappropriate the real power PI controller control parameters considering ITAE as the performancecriterion. The possible limitation of the proposed method is that the fuzzy controller solution isspecifically for the ITAE performance criterion. However, the fuzzy controller may provide varyingsolutions if different performance criteria, such as integral absolute error (IAE), and integral squareerror (ISE), were used.
On the whole, a power management system for a grid-connected hybrid system consisting ofsolar PV and SOFC is proposed considering varying loads and solar radiation. In order to operatethe SOFC efficiently within a specific power range and to deliver the power set by the reference set point,a fuzzy logic controller is also developed to generate appropriate control parameters for the PI controller.The performance of the controllers is evaluated by the minimizing ITAE criterion for a 24 h time period.
5. Simulation Results
5.1. Optimization of Control Parameters
The objective of the SOFC active power controller is to deliver a power set by the reference (PFCref),which is generated from the power management module. The control parameters of the controller areevaluated using the GA and simplex method. The PSCAD program is equipped with the optimum runsearch engine module, which enables us to perform successive simulations for a group of parameters.The group of parameters generated by the optimization algorithm is used for simulation program andsimultaneously evaluates the objective function given in Equation (14). The GA and simplex methodpresent in the optimum run module were used for this study. A generalized simulation flow for the GAand simplex method is presented in Figure 8. The search is terminated when the stopping criterion ismet, that is, when the algorithm completes the maximum number of iterations.
The fuel cell reference set point (PFCref) changes at regular intervals due to changes in load andPV input power. The PI controller parameters are optimized for the SOFC reference set points (PFCref)for every hour. The final optimized values for different fuel cell reference set points are used for the
Energies 2017, 10, 1720 11 of 17
simulation. Therefore the optimal parameters found using the GA or simplex method for differentreference set points will be used throughout the simulation. The dynamic change in the controllerparameters for the simplex and GA optimization methods for different fuel cell set points are shown inFigures 9 and 10, respectively.
Energies 2017, 10, 1720 11 of 17
simulation. Therefore the optimal parameters found using the GA or simplex method for different
reference set points will be used throughout the simulation. The dynamic change in the controller
parameters for the simplex and GA optimization methods for different fuel cell set points are shown
in Figures 9 and 10, respectively.
Figure 8. Generalized optimization flow using the optimum run module in PSCAD.
(a)
(b)
Figure 9. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points
using the simplex method.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 231.8
2
2.2
2.4
2.6
2.8
3
3.2
Time in hours
Kp
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230
0.1
0.2
0.3
0.4
0.5
Time in hours
Ti
Figure 8. Generalized optimization flow using the optimum run module in PSCAD.
Energies 2017, 10, 1720 11 of 17
simulation. Therefore the optimal parameters found using the GA or simplex method for different
reference set points will be used throughout the simulation. The dynamic change in the controller
parameters for the simplex and GA optimization methods for different fuel cell set points are shown
in Figures 9 and 10, respectively.
Figure 8. Generalized optimization flow using the optimum run module in PSCAD.
(a)
(b)
Figure 9. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points
using the simplex method.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 231.8
2
2.2
2.4
2.6
2.8
3
3.2
Time in hours
Kp
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230
0.1
0.2
0.3
0.4
0.5
Time in hours
Ti
Figure 9. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set pointsusing the simplex method.
Energies 2017, 10, 1720 12 of 17Energies 2017, 10, 1720 12 of 17
(a)
(b)
Figure 10. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points
using genetic algorithm (GA).
The Kp and Ti generated by the FIS system is shown in Figure 11 for different values of input
(PFCref).
(a)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time in hours
Kp
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time in hours
Ti
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5
1
1.5
2
2.5
3
Time in hours
Kp
Figure 10. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set pointsusing genetic algorithm (GA).
The Kp and Ti generated by the FIS system is shown in Figure 11 for different values ofinput (PFCref).
Energies 2017, 10, 1720 12 of 17
(a)
(b)
Figure 10. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points
using genetic algorithm (GA).
The Kp and Ti generated by the FIS system is shown in Figure 11 for different values of input
(PFCref).
(a)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time in hours
Kp
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time in hours
Ti
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.5
1
1.5
2
2.5
3
Time in hours
Kp
Figure 11. Cont.
Energies 2017, 10, 1720 13 of 17Energies 2017, 10, 1720 13 of 17
(b)
Figure 11. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points
using the fuzzy‐based PI controller.
The ranges of optimal control parameters for the PI controller were obtained using the GA,
simplex method and fuzzy logic system are summarized in Table 2.
Table 2. Optimal Kp and Ti ranges found using the GA, simplex method and fuzzy logic control.
Method Control Parameter and Objective Function
Kp Ti ITAE
GA 0.750–4.958 0.0217–1.550 7844.99311
Simplex 1.966–3.097 0.0087–0.5247 483.79171
PSCAD‐MATLAB fuzzy logic control 1–3 0.013–0.047 73.3385
In Table 2, the objective function evaluated for the fuzzy logic controller is lower than the other
methods. This proves that that fuzzy‐logic‐based PI controller is efficient. In addition, the controller’s
capability to dispatch SOFC power (PFC) matching its reference value (PFCref) can be seen in Figure 12.
Figure 12. Comparison of SOFC power dispatch (PFC) matching the reference (PFCref) for the controllers.
The SOFC reference set point (PFCref) is dependent on the change in load and PV generation. With
reference to Figure 12, it can be seen that during the early morning hours when the PV power is zero,
the fuzzy‐based PI controller efficiently controls its power supply to the reference value for load
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Time in hours
Ti
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
Time in hours
Pow
er i
n M
W
PFC obtained using fuzzy based PI controlPFC obtained using optimal operation of simplexPFC obtained using optimal operation of GAPFCref
Figure 11. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set pointsusing the fuzzy-based PI controller.
The ranges of optimal control parameters for the PI controller were obtained using the GA,simplex method and fuzzy logic system are summarized in Table 2.
Table 2. Optimal Kp and Ti ranges found using the GA, simplex method and fuzzy logic control.
MethodControl Parameter and Objective Function
Kp Ti ITAE
GA 0.750–4.958 0.0217–1.550 7844.99311Simplex 1.966–3.097 0.0087–0.5247 483.79171
PSCAD-MATLAB fuzzy logic control 1–3 0.013–0.047 73.3385
In Table 2, the objective function evaluated for the fuzzy logic controller is lower than the othermethods. This proves that that fuzzy-logic-based PI controller is efficient. In addition, the controller’scapability to dispatch SOFC power (PFC) matching its reference value (PFCref) can be seen in Figure 12.
Energies 2017, 10, 1720 13 of 17
(b)
Figure 11. (a,b) show the variation of Kp and Ti respectively for different fuel cell controller set points
using the fuzzy‐based PI controller.
The ranges of optimal control parameters for the PI controller were obtained using the GA,
simplex method and fuzzy logic system are summarized in Table 2.
Table 2. Optimal Kp and Ti ranges found using the GA, simplex method and fuzzy logic control.
Method Control Parameter and Objective Function
Kp Ti ITAE
GA 0.750–4.958 0.0217–1.550 7844.99311
Simplex 1.966–3.097 0.0087–0.5247 483.79171
PSCAD‐MATLAB fuzzy logic control 1–3 0.013–0.047 73.3385
In Table 2, the objective function evaluated for the fuzzy logic controller is lower than the other
methods. This proves that that fuzzy‐logic‐based PI controller is efficient. In addition, the controller’s
capability to dispatch SOFC power (PFC) matching its reference value (PFCref) can be seen in Figure 12.
Figure 12. Comparison of SOFC power dispatch (PFC) matching the reference (PFCref) for the controllers.
The SOFC reference set point (PFCref) is dependent on the change in load and PV generation. With
reference to Figure 12, it can be seen that during the early morning hours when the PV power is zero,
the fuzzy‐based PI controller efficiently controls its power supply to the reference value for load
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Time in hours
Ti
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
Time in hours
Pow
er i
n M
W
PFC obtained using fuzzy based PI controlPFC obtained using optimal operation of simplexPFC obtained using optimal operation of GAPFCref
Figure 12. Comparison of SOFC power dispatch (PFC) matching the reference (PFCref) for the controllers.
The SOFC reference set point (PFCref) is dependent on the change in load and PV generation.With reference to Figure 12, it can be seen that during the early morning hours when the PV power is
Energies 2017, 10, 1720 14 of 17
zero, the fuzzy-based PI controller efficiently controls its power supply to the reference value for loadchanges. It should also be noticed in Figure 12 that the fuel cell reference changes suddenly between6 a.m. to 7 a.m. due to the sudden increase in load demand from 40 kW to 54 kW, and during this timeperiod the PV power is absent. SOFC controllers tuned by the GA, fuzzy and simplex method werecapable of following the SOFC reference set point for the sudden load increase. Between 8 a.m. and7 p.m. the fuel cell reference is regulated to 20 kW for two reasons (i) during this period PV poweris available, and is more than sufficient to supply the varying load demand; and (ii) the fuel cell hasto operate within its specific power limit. Between 7 a.m. and 8 a.m. the PFCref is regulated to 20 kW,where the fuzzy controller follows the reference line exactly, but the controllers based on the GA andsimplex method take time to settle at the reference value. Further, the fuzzy-based PI controller ismore efficient after 7 p.m. that is, after sunset. After sunset, the load demand is taken care of bythe SOFC. The fuzzy-based PI controller efficiently dispatches power from the SOFC to its referencevalue from 7 p.m., thereafter supplying the peak load at 9 p.m. On the other hand, the simplexmethod and GA-based PI controller was found to be less efficient in following the reference value.The fuzzy-logic-based PI controller’s efficiency is tested during the absence of PV power.
Figure 12 shows that the SOFC controlled by a fuzzy-based PI controller is efficient where the fuelcell power (PFC) follows the reference (PFCref). It should be noted that in all the three controller types,the fuel cell is operating within its specific power range.
5.2. Application of Fuzzy-Based PI Controller for Power Management System
The results from the previous section confirmed that the fuzzy-based PI controller for SOFC activepower control is more efficient. Therefore, a simulation of the power management system was carriedout using the PSCAD-Matlab interface for the fuzzy-based PI controller for SOFC active power controlfor the hybrid system shown in Figure 1.
Load modeling is one of the important parts of a power system. Load varies throughout the dayand in some hours of the day the load reaches its maximum value and/or minimum value. In thiswork, a variable residential load is modeled with a maximum load demand reaching up to 100 kW.The daily load pattern of a residential area from [29] is used for this work. The load pattern is scaledup to a maximum load demand of 100 kW; see Figure 13.
The simulation results for the power management strategy are shown in Figure 14. Figure 14adescribes overall operating strategy of the hybrid system considering changes in load and solarradiation levels. The SOFC supplies power based on its reference value shown in Figure 12. Figure 14bshows the actual power generated from hybrid system which follows the reference.
Energies 2017, 10, 1720 14 of 17
changes. It should also be noticed in Figure 12 that the fuel cell reference changes suddenly between
6 a.m. to 7 a.m. due to the sudden increase in load demand from 40 kW to 54 kW, and during this
time period the PV power is absent. SOFC controllers tuned by the GA, fuzzy and simplex method
were capable of following the SOFC reference set point for the sudden load increase. Between 8 a.m.
and 7 p.m. the fuel cell reference is regulated to 20 kW for two reasons (i) during this period PV power
is available, and is more than sufficient to supply the varying load demand; and (ii) the fuel cell has
to operate within its specific power limit. Between 7 a.m. and 8 a.m. the PFCref is regulated to 20 kW,
where the fuzzy controller follows the reference line exactly, but the controllers based on the GA and
simplex method take time to settle at the reference value. Further, the fuzzy‐based PI controller is
more efficient after 7 p.m. that is, after sunset. After sunset, the load demand is taken care of by the
SOFC. The fuzzy‐based PI controller efficiently dispatches power from the SOFC to its reference
value from 7 p.m., thereafter supplying the peak load at 9 p.m. On the other hand, the simplex method
and GA‐based PI controller was found to be less efficient in following the reference value. The fuzzy‐
logic‐based PI controller’s efficiency is tested during the absence of PV power.
Figure 12 shows that the SOFC controlled by a fuzzy‐based PI controller is efficient where the
fuel cell power (PFC) follows the reference (PFCref). It should be noted that in all the three controller
types, the fuel cell is operating within its specific power range.
5.2. Application of Fuzzy‐Based PI Controller for Power Management System
The results from the previous section confirmed that the fuzzy‐based PI controller for SOFC
active power control is more efficient. Therefore, a simulation of the power management system was
carried out using the PSCAD‐Matlab interface for the fuzzy‐based PI controller for SOFC active
power control for the hybrid system shown in Figure 1.
Load modeling is one of the important parts of a power system. Load varies throughout the day
and in some hours of the day the load reaches its maximum value and/or minimum value. In this
work, a variable residential load is modeled with a maximum load demand reaching up to 100 kW.
The daily load pattern of a residential area from [29] is used for this work. The load pattern is scaled
up to a maximum load demand of 100 kW; see Figure 13.
The simulation results for the power management strategy are shown in Figure 14. Figure 14a
describes overall operating strategy of the hybrid system considering changes in load and solar
radiation levels. The SOFC supplies power based on its reference value shown in Figure 12. Figure
14b shows the actual power generated from hybrid system which follows the reference.
Figure 13. Daily load profile.
From Figure 14a it is clear that the power from the SOFC is well managed during the presence
and absence of PV power. When PV power is zero in the early morning hours and after sunset in the
evening, any change in the load is supplied by the SOFC. Since PV power is available during the day,
it supplies the required power needed by the load. During the day, the excess power generated from
the hybrid system is injected into the grid, where the power injection into the grid is indicated in the
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Pow
er in
kW
Time in hours
Figure 13. Daily load profile.
From Figure 14a it is clear that the power from the SOFC is well managed during the presenceand absence of PV power. When PV power is zero in the early morning hours and after sunset inthe evening, any change in the load is supplied by the SOFC. Since PV power is available during
Energies 2017, 10, 1720 15 of 17
the day, it supplies the required power needed by the load. During the day, the excess power generatedfrom the hybrid system is injected into the grid, where the power injection into the grid is indicatedin the negative in Figure 14a. If the availability of PV power is less, the power deficit required bythe load is taken care of by the SOFC. Here, the reference value for the SOFC is calculated as explainedin Section 3 and is generated by the power management module.
During the entire period of operation of the hybrid system, the SOFC power PFC changes based onthe reference value PFCref generated by the power management module, at the same time the PV arrayoperates at the maximum power point. In addition, the power imported from the grid is almost zero,which can be established from Figure 14a, where the grid power is zero or negative during the entireoperating time. From Figure 12 it is clear that the SOFC is operating within its operating range of20 kW to 100 kW. With reference to these results, it is clear that the operating strategy is simple andthat the fuzzy-based PI controller for SOFC active power control is more efficient.
It should also be noted that apart from the fuel cell, the proposed fuzzy based PI control can beapplied to any electronically-interfaced controllable distributed energy source, such as battery energysystems or capacitors.
Energies 2017, 10, 1720 15 of 17
negative in Figure 14a. If the availability of PV power is less, the power deficit required by the load
is taken care of by the SOFC. Here, the reference value for the SOFC is calculated as explained in
Section 3 and is generated by the power management module.
During the entire period of operation of the hybrid system, the SOFC power PFC changes based
on the reference value PFCref generated by the power management module, at the same time the PV
array operates at the maximum power point. In addition, the power imported from the grid is almost
zero, which can be established from Figure 14a, where the grid power is zero or negative during the
entire operating time. From Figure 12 it is clear that the SOFC is operating within its operating range
of 20 kW to 100 kW. With reference to these results, it is clear that the operating strategy is simple
and that the fuzzy‐based PI controller for SOFC active power control is more efficient.
It should also be noted that apart from the fuel cell, the proposed fuzzy based PI control can be
applied to any electronically‐interfaced controllable distributed energy source, such as battery energy
systems or capacitors.
(a)
(b)
Figure 14. Simulation results of the power management system. (a) Overall system operating strategy;
(b) Hybrid system reference and actual value.
6. Conclusions and Future Work
In this study, a power management strategy for a grid‐connected hybrid PV‐SOFC system
supplying power at varying loads is presented. The optimal control parameters of the PI controller
used in SOFC active power control were found using the GA and simplex method. In addition, a
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23-0.18-0.16-0.14-0.12-0.1
-0.08-0.06-0.04-0.02
00.020.040.060.080.1
0.120.140.160.180.2
Time in hours
Pow
er i
n M
W
PFCPGridPLoadPPV
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 230
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Time in hours
Pow
er i
n M
W
PHybrefPHyb
Figure 14. Simulation results of the power management system. (a) Overall system operating strategy;(b) Hybrid system reference and actual value.
Energies 2017, 10, 1720 16 of 17
6. Conclusions and Future Work
In this study, a power management strategy for a grid-connected hybrid PV-SOFC systemsupplying power at varying loads is presented. The optimal control parameters of the PI controllerused in SOFC active power control were found using the GA and simplex method. In addition,a PSCAD-Matlab interface fuzzy-based PI controller was also designed to generate the optimal controlparameters for changing input.
A comparison between the three methods was performed where the GA and simplex methodSOFC active power controllers were found to be less efficient. The fuzzy-logic-based controllerensured that the output power from the SOFC followed the reference value accurately. Using thispower management strategy, the following objectives were achieved: (i) the SOFC always operateswithin a specific power range; and (ii) the power drawn from the grid is zero at all times. Operatingthe SOFC within its specific operating range increases the efficiency of the fuel cell and also enhancesthe performance of the system. The hybrid system can increase its generation when the load is heavyand decrease its generation when the load is light. In brief, the grid-connected hybrid system worksflexibly with this operating strategy. For further consideration, the proposed fuzzy logic will beimplemented for (i) effective real power control of a battery bank; and (ii) voltage and reactive powercontrol of controllable DGs.
Acknowledgments: This work was supported by the Ministry of Education Malaysia (HIR-MOHED000004-16001).
Author Contributions: Hazlie Moklis and Saad Mekhilef conceived and designed the experiments; ShivashankarSukumar performed the experiments; Marayati Marsadek and Agileswari Ramasamy analyzed the data;Shivashankar Sukumar wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. Ren, P.S. Renewables 2015 Global Status Report; REN21 Secretariat: Paris, France, 2015.2. Hassmann, K. SOFC power plants, the Siemens-Westinghouse approach. Fuel Cells 2001, 1, 78–84. [CrossRef]3. Hatti, M.; Meharrar, A.; Tioursi, M. Power management strategy in the alternative energy photovoltaic/PEM
Fuel Cell hybrid system. Renew. Sustain. Energy Rev. 2011, 15, 5104–5110. [CrossRef]4. El-Shater, T.F.; Eskander, M.N.; El-Hagry, M.T. Energy flow and management of a hybrid wind/PV/fuel cell
generation system. Int. J. Sustain. Energy 2006, 25, 91–106. [CrossRef]5. Khanh, L.N.; Seo, J.J.; Kim, Y.S.; Won, D.J. Power-management strategies for a grid-connected PV-FC hybrid
system. IEEE Trans. Power Deliv. 2010, 25, 1874–1882. [CrossRef]6. Wang, C.; Nehrir, M.H. Power Management of a standalone Wind/PV/FC energy system. IEEE Trans.
Energy Convers. 2008, 23, 957–967. [CrossRef]7. Taher, S.A.; Mansouri, S. Optimal PI controller design for active power in grid-connected SOFC DG system.
Int. J. Electr. Power Energy Syst. 2014, 60, 268–274. [CrossRef]8. Anantwar, H.; Lakshmikantha, B.R.; Sundar, S. Fuzzy self tuning PI controller based inverter control for
voltage regulation in off-grid hybrid power system. Energy Procedia 2017, 117, 409–416. [CrossRef]9. Mishra, S.; Sahoo, S.; Dugar, A. Hybrid MVMO based controller for energy management in a grid connected
DC microgrid. In Proceedings of the IEEE Power, Communication and Information Technology Conference,Bhubaneswar, India, 15–17 October 2015; pp. 114–119.
10. Al-Saedi, W.; Lachowicz, S.W.; Habibi, D.; Bass, O. Power flow control in grid-connected microgrid operationusing particle swarm optimization under variable load conditions. Int. J. Electr. Power Energy Syst. 2013, 49,76–85. [CrossRef]
11. Laghari, J.A.; Mokhlis, H.; Bakar, A.; Mohamad, H. A fuzzy based load frequency control for distributionnetwork connected with mini hydro power plant. J. Intell. Fuzzy Syst. 2014, 26, 1301–1310.
12. Ozbay, E.; Gencoglu, M.T. Load frequency control for small hyrdo power plants using adaptive fuzzycontroller. In Proceedings of the IEEE International Conference on Systems Man and Cybermetrics (SMC),Istanbul, Turkey, 10–13 October 2010; pp. 1–5.
Energies 2017, 10, 1720 17 of 17
13. Mohagheghi, S.; Harley, R.G.; Venayagamoorthy, G.K. Modified Takagi-Sugeno fuzzy logic based controllersfor a static compensator in a multimachine power system. In Proceedings of the Conference Record ofthe IEEE 39th IAS Annual Meeting Industry Applications Conference, Seattle, WA, USA, 3–7 October 2004;pp. 2637–2642.
14. Kassem, A.M.; Zaid, S.A. Load parameter waveforms improvement of a stand-alone wind-based energystorage system and Takagi–Sugeno fuzzy logic algorithm. IET Renew. Power Gener. 2014, 8, 775–785.[CrossRef]
15. Luk, P.C.K.; Low, K.C.; Sayiah, A. GA-based fuzzy logic control of a solar power plant using distributedcollector fields. Renew. Energy 1999, 16, 765–768. [CrossRef]
16. Syed, F.U.; Ying, H.; Kuang, M.; Okubo, S.; Smith, M. Rule-Based Fuzzy Gain-Scheduling PI Controllerto Improve Engine Speed and Power Behavior in a Power-split Hybrid Electric Vehicle. In Proceedingsof the IEEE Annual Meeting of the North American Fuzzy Information Processing Society, Montreal, QC,Canada, 3–6 June 2006; pp. 284–289.
17. Berrazouane, S.; Mohammedi, K. Parameter optimization via cuckoo optimization algorithm of fuzzycontroller for energy management of a hybrid power system. Energy Convers. Manag. 2014, 78, 652–660.[CrossRef]
18. Letting, L.K.; Munda, J.L.; Hamam, Y. Optimization of a fuzzy logic controller for PV grid inverter controlusing S-function based PSO. Sol. Energy 2012, 86, 1689–1700. [CrossRef]
19. Yazdani, A.; Di Fazio, A.R.; Ghoddami, H.; Russo, M.; Kazerani, M.; Jatskevich, J.; Strunz, K.; Leva, S.;Martinez, J. Modeling guidelines and a benchmark for power system simulation studies of three-phasesingle-stage photovoltaic systems. IEEE Trans. Power Deliv. 2011, 26, 1247–1264. [CrossRef]
20. Rajapakse, A.D.; Muthumuni, D. Simulation tools for photovoltaic system grid integration studies.In Proceedings of the IEEE Electrical Power and Energy Conference (EPEC), Montreal, QC, Canada,22–23 October 2009; pp. 1–5.
21. Koohi-Kamali, S.; Rahim, N.A.; Mokhlis, H. Smart power management algorithm in microgrid consisting ofphotovoltaic, diesel, and battery storage plants considering variations in sunlight, temperature, and load.Energy Convers. Manag. 2014, 84, 562–582. [CrossRef]
22. Eltawil, M.A.; Zhao, Z. MPPT techniques for photovoltaic applications. Renew. Sustain. Energy Rev. 2013, 25,793–813. [CrossRef]
23. Larminie, J.; Dicks, A. Fuel Cell Systems Explained; John Wiley & Sons Ltd.: West Sussex, UK, 2003.24. Fedakar, S.; Bahceci, S.; Yalcinoz, T. Modeling and simulation of grid connected solid oxide fuel cell using
PSCAD. J. Renew. Sustain. Energy 2014, 6, 053118. [CrossRef]25. Zhu, Y.; Tomsovic, K. Development of models for analyzing the load-following performance of microturbines
and fuel cells. Electr. Power Syst. Res. 2002, 62, 1–11. [CrossRef]26. Wang, X.; Huang, B.; Chen, T. Data-driven predictive control for solid oxide fuel cells. J. Process Control
2007, 17, 103–114. [CrossRef]27. Li, Y.H.; Rajakaruna, S.; Choi, S.S. Control of a solid oxide fuel cell power plant in a grid-connected system.
IEEE Trans. Energy Convers. 2007, 22, 405–413. [CrossRef]28. Maiti, D.; Acharya, A.; Chakraborty, M.; Konar, A.; Janarthanan, R. Tuning PID and PI/λ D δ Controllers
Using the Integral Time Absolute Error Criterion. In Proceedings of the IEEE 4th International ConferenceInformation and Automation for Sustainability (ICIAFS), Colombo, Sri Lanka, 12–14 December 2008;pp. 457–462.
29. Lau, K.Y.; Yousof, M.F.M.; Arshad, S.N.M.; Anwari, M.; Yatim, A.H.M. Performance analysis of hybridphotovoltaic/diesel energy system under Malaysian conditions. Energy 2010, 35, 3245–3255. [CrossRef]
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